45.2.17 problem 17

Internal problem ID [7240]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section : Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page 239
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:48:47 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 44

Order:=6; 
dsolve(4*x*diff(y(x),x$2)+1/2*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{{7}/{8}} \left (1-\frac {2}{15} x +\frac {2}{345} x^{2}-\frac {4}{32085} x^{3}+\frac {2}{1251315} x^{4}-\frac {4}{294059025} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (1-2 x +\frac {2}{9} x^{2}-\frac {4}{459} x^{3}+\frac {2}{11475} x^{4}-\frac {4}{1893375} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 83

AsymptoticDSolveValue[4*x*D[y[x],{x,2}]+1/2*D[y[x],x]+y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (-\frac {4 x^5}{1893375}+\frac {2 x^4}{11475}-\frac {4 x^3}{459}+\frac {2 x^2}{9}-2 x+1\right )+c_1 x^{7/8} \left (-\frac {4 x^5}{294059025}+\frac {2 x^4}{1251315}-\frac {4 x^3}{32085}+\frac {2 x^2}{345}-\frac {2 x}{15}+1\right ) \]